...is that it's so unbelievably stupid at this point in history.
At one point in time, glass ceilings and career ladders to these sorts of jobs really did limit the supply of qualified female candidates. You could cite discrimination and other disparities as the fundamental cause, but there really was a lack of qualified female candidates, and given a lack of qualified female candidates one really could worry about "whether gender plays a role" in the decision.
But that's not the case today. There are at least two tremendous female candidates. Supply constraints on female central bankers are still a problem but we've passed that point where one has to even have a hint of a concern about whether "gender drives the appointment". It's stupid. It doesn't. There's no question at all that Yellen or Romer would be well qualified.
That's the saddest thing: not even the claim itself so much as the fact that it is invoked when these two are in the running. Massive fail.
Ditto the Supreme Court by the way. What the hell do you care if we have nine women on the court at this point? The candidates for the job are clearly equal to the task and that, I would have thought, closes the discussion. We are well past the time when the supply of qualified women might have been questionable enough to raise these concerns. The fact that these concerns persist, I think, is really starting to show peoples' true colors.